A color is a light flow perceived by the human eye. It is a spectral energy distribution on a wavelength band, in this case 380 to 780 nm for the visible spectrum. Professional digital spectrophotometers currently measure these distributions with a pitch of five nm, or eighty-one values for the visible spectrum. Hereinafter, we will use a letter and a λ in parentheses to designate the eighty-one values that describe a spectral energy distribution S(λ) in the visible spectrum. This curve S(λ) may be interpolated with a reduced number of points [λi, S(λ)i], in the case at hand for the rest of this document a sealed cubic spline function with zero slopes at 380 and 780 nm.
Due to the additive synthesis, any color may be expressed by its trichromatic coordinates using three primary colors. There are several systems of primaries; hereinafter, we will use the two normalized sets, namely the CIE XYZ space (and its alternative CIE xyY with the constant-luminance chromaticity plan) and the CIE L*a*b space, which allows an accurate estimation of the color difference with a Euclidean norm called “deltaE”. The “gamut” (limits) of these two spaces covers the entire spectrum visible to humans. We will also refer to the sRGB trichromatic space corresponding to the reference gamut for most of the current electronic equipment. The sRGB gamut does not cover the entire spectrum visible to humans, in particular in the blue-greens.
The color of an object is the spectrum C(λ) equal to the product of an illuminant I(λ) reflecting on a surface whose spectral reflectance is R(λ).
In other words, the color of an object may be characterized by its CIE XYZ or L*a*b trichromatic coordinates for a given illuminant (example: D65 or D50) or, better, by its spectral reflectance R(λ). This second method has the interest of being able to simulate the perception of the color under different illuminance (inside, outside). This is the color chart method: the user places the color chart next to the object and seeks, by iteration, the color from the chart that is closest to the color of the object, for example the Pantone Matching System (registered trademark for color names) or the RAL (Reichsausschulβ für Lieferbedingungen), which is a color codification system developed in 1927 by the German Institute for quality assurance and the associated marking.
The major interest of the charts is that they are much more precise/faithful in characterizing the color of an object than trichromatic coordinates (in particular to eliminate metamerism and provide information on the surface state: brilliance, roughness, etc.), while offering an encoding and storage system that is as simple as the trichromatic coordinates owing to the familiarity of the name and/or alphanumeric code. The major drawback of charts relative to trichromatic coordinates under a given illuminant lies in the relative and discontinuous/discrete nature of the storage of the information, i.e., a dictionary is necessary to establish a correspondence/communication between a spectrophotometric measurement and the codes of a color chart, to determine the equivalencies between the different color chart systems themselves (for example: transition from the Pantone name to a RAL code, etc.), and to have explicit data in order to simulate the behavior of a color, for example in 3D computer simulations.
Faced with these shortcomings, 3D programming has led to the development of many spectral reflectance models R(λ) to characterize surface renderings in order to create virtual objects with a realistic appearance (applications to architecture, for example) or to archive the characteristics of actual objects (virtual museums, e-commerce), to depict them with arbitrary lighting conditions and viewing angles. A new constraint, the simplicity of the formulation, has appeared jointly so that the choice or measurement of the descriptive parameters is easy and the calculations necessary for rendering of the synthesis images are done in a reasonable amount of time. The most widely known models are those, inter alia, of Lambert, Phong, Torrance and Sparrow, Beckmann and Spizzichino, Oren and Nayar, Ward, Ashikhmin, He, etc. They are based on image models or acquisition (example: gonioreflectometer).
All of these models have one point in common: the spectral reflectance that models the surface of the object is qualified as “bidirectional” in that it varies not only as a function of the wavelengths making up the illuminant, but also as a function of the incidence angle with which the illuminant strikes the surface and the incidence angle with which the viewer or camera views the surface. In fact, the incident light on the surface of a given object may interact with it differently. In the case of an opaque surface, three phenomena compete to give the material the appearance it is known for: absorption, reflection and diffusion.
In reference to the works by He, which are the most developed, the final expression of the bidirectional reflectance is broken down into three terms: specular (s)/specular peak, directional diffuse (dd)/specular lobe, uniform diffuse (du)—as illustrated in FIG. 1:Rbd(λ,L,V,N)=Rbd,s+Rbd,dd+Rbd,du 
The specular reflection or specular peak occurs on the surface of the object. The light is reflected in the theoretical direction defined by the Snell-Descartes laws. There is very little interaction of light with the material of the object, and in particular its pigments. The color of the reflected light is therefore close to the color of the received light (e.g.: mirror, high gloss paint). The specular component of He comes from the unique reflection of the light on the average level of the surface. In the case of a smooth surface, this component predominates the others and a specular peak is indeed observed.
The directional diffuse or specular lobe reflection corresponds to the light reflected inside a cone/lobe centered on that same direction of the Snell-Descartes laws (e.g.: satin paint). The directional diffuse component is due to the unique reflection of the light on the roughness of the surface (diffraction phenomenon).
The uniform diffuse reflection takes place on a deeper level and the emitted light is tinted by the color of the pigments (e.g.: matte paint). This third component is attributed to the multiple reflections and the interactions of the light with the surface material.
The interest of the bidirectional spectral reflectance models is their capacity to characterize the color of an object as faithfully as a color chart (for example: multispectral color, brilliance, roughness, etc.) while offering storage of the information that is both absolute and continuous, in the sense that no dictionary is necessary to establish a correspondence/communication between a spectrophotometric measurement and the codes of a color chart, to determine equivalencies between the different color chart systems themselves (for example: transition from a Pantone name to a RAL code, etc.) and have explicit data in order to simulate the behavior of a color. The major drawback of these models is that they require a significant quantity of information that is impossible for an individual to remember and/or to store easily on a paint can in a display (for example: barcode or chip). Several methods have been proposed to compress the data resulting from a direct measurement (or a simulation from a microscopic geometric surface model) of the bidirectional reflectance: the spherical harmonics, lengths affixed on a geodesic sphere or spherical wavelets. These also require improvements, since they again have the double drawback of requiring large storage capacities and long computation times.
The following are known from the state of the art:                Application PCT WO 2006/093376, which describes a method for generating a barcode.        European patent no. EP 0,961,475, which relates to a rendering apparatus, multispectral image scanner and automatic three-dimensional goniospectrophotometer. However, this European patent only pertains to the acquisition of the bidirectional spectral reflectance, and not its adaptive compressed storage.        In the field of compression by spherical harmonics, the following scientific publication: B. Cabral, N. Max, R. Springmeyer. “Bidirectional reflection functions from surface bump maps”. SIGGRAPH '87 (1987), pp. 273-281.        In the field of compression by spherical harmonics, the following scientific publication: S. H. Westin, J. R. Arvo, K. E. Torrance. “Predicting reflectance functions from complex surfaces”. SIGGRAPH '92 (1992), pp. 255-264.        In the field of compression by lengths affixed on a geodesic sphere, the following scientific publication: J. S. Gondek, G. W. Meyer, J. G. Newman. “Wavelength dependent reflectance functions”. SIGGRAPH '94 (1994), pp. 213-220.        In the field of compression by spherical wavelets, the following scientific publication: Schröder, W. Sweldens. “Spherical wavelets: Efficiently represented functions on the sphere”. SIGGRAPH '95 (1995).        